What is the length of time before melanoma metastasizes?

Variable. Early melanoma may be surgically cured and never metastasize. Melanoma with poor risk features such as deep, ulcerated, or involving lymph nodes has a higher risk of metastasizing. Additionally, new melanomas may form on someone that has already developed one. Followup with your dermatologist, surgeon, etc. Is recommended to find any early and decrease risk.
Depends on depth. The risk of spread of melanoma depends on depth of its growth. Some tumor tend to grow superficially, and therefore do not metastasize. Others grow deep quickly, so a relatively small lesion may metastasize early in that case. If you suspect a melanoma, have it evaluated asap. See my skin cancer health guide. Best wishes!
Varies. Different tumor gain the ability to metastasize at different rates. It is impossible to predict.
Very variable. If melanoma metastasizes it is generally within the first year and a half or two years after diagnosis. However melanoma has recurred decades after initial surgery.